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Quantum Dynamics in Classical Spin Baths

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of the density matrix. The weak coupling limit of the equation can be integrated by standard algorithms and provides a non-Markovian approach to the computer simulation of quantum systems in classical spin environments. It is expected that the theory and numerical schemes presented here have a wide applicability.